The Minimum Wage and Inequality The Effects of Education and Technology

Zs´ ofia L. B´ar´any Sciences Po

2013 March

Zs´ ofia L. B´ ar´ any (Sciences Po)

The Minimum Wage and Inequality

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Motivation Question: What is the contribution of falling minimum wages to increasing inequality? Which are the important channels?

Zs´ ofia L. B´ ar´ any (Sciences Po)

The Minimum Wage and Inequality

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Motivation Question: What is the contribution of falling minimum wages to increasing inequality? Which are the important channels? Increasing wage inequality in the US since the 1970s particularly sharp during the 1980s graph One prominent explanation: change in labour market institutions In particular the decrease in real federal minimum wages

graph

The effects of minimum wages are usually analyzed in partial equilibrium models minimum wage truncates the distribution and only affects those for who it is close to binding → Correlation of minimum wage and upper tail inequality purely coincidental Zs´ ofia L. B´ ar´ any (Sciences Po)

The Minimum Wage and Inequality

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Fig. 23.—Wage inequality and the minimum wage

Source: Card and DiNardo (2002). Zs´ ofia L. B´ ar´ any (Sciences Po)

The Minimum Wage and Inequality

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5

5

.55

.6

.65

Log Points .7

.75

.8

Log 90/50 Hourly Earnings Inequality and Real Minimum Wage

90/50 Gap = 1.51 (0.14) - 0.48 (0.08) x MinWage, R-Squared=0.52

1973

1977

1981

1985

1989

90-50 Wage Gap

1993

1997

2001

2005

E(90-50 Gap | Min Wage)

/50 and 50/10 Hourly Wage Differentials, 1973-2005 (May/ORG CPS).

deflator. In the first panel, the real log minimum wage measure is normalized to zero nd 50/10) for all hourly workers from the May/ORG CPS samples in each year plotted t wage and the contemporaneous log minimum wage. Zs´ ogap fia L. on B´ ar´ aa ny constant (Sciences Po) The Minimum Wage and real Inequality

Source: Autor, Katz and Kearney (2008).

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Main contributions Show that the min wage affects skill prices, which change the incentives that people face when making educational decisions General equilibrium model that allows the full quantitative analysis of the effects of minimum wages Bridges two of the most prominent explanations for increasing inequality: skill-biased technical change and labour market institutions Theoretical contribution: allows both technology and relative labour supply to adjust endogenously → reveals that the interaction of minimum wages and education is important In such a framework a change in the minimum wage affects the entire wage distribution Zs´ ofia L. B´ ar´ any (Sciences Po)

The Minimum Wage and Inequality

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Key Ingredients Two sector production economy

Minimum wage

Endogenous skill acquisition

Endogenous technology

Zs´ ofia L. B´ ar´ any (Sciences Po)

The Minimum Wage and Inequality

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Key Ingredients Two sector production economy I I

high-skilled workers work in one sector, low-skilled workers in the other the two goods they produce are imperfect substitutes

Minimum wage

Endogenous skill acquisition

Endogenous technology

Zs´ ofia L. B´ ar´ any (Sciences Po)

The Minimum Wage and Inequality

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Key Ingredients Two sector production economy I I

high-skilled workers work in one sector, low-skilled workers in the other the two goods they produce are imperfect substitutes

Minimum wage I

I

workers with marginal product lower than the minimum wage are unemployed everyone else employed in the sector relevant for their skill

Endogenous skill acquisition

Endogenous technology

Zs´ ofia L. B´ ar´ any (Sciences Po)

The Minimum Wage and Inequality

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Key Ingredients Two sector production economy I I

high-skilled workers work in one sector, low-skilled workers in the other the two goods they produce are imperfect substitutes

Minimum wage I

I

workers with marginal product lower than the minimum wage are unemployed everyone else employed in the sector relevant for their skill

Endogenous skill acquisition I

individuals make educational decisions optimally - based on idiosyncratic cost and ability

Endogenous technology

Zs´ ofia L. B´ ar´ any (Sciences Po)

The Minimum Wage and Inequality

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Key Ingredients Two sector production economy I I

high-skilled workers work in one sector, low-skilled workers in the other the two goods they produce are imperfect substitutes

Minimum wage I

I

workers with marginal product lower than the minimum wage are unemployed everyone else employed in the sector relevant for their skill

Endogenous skill acquisition I

individuals make educational decisions optimally - based on idiosyncratic cost and ability

Endogenous technology I

I

technical change is based on choices made by firms about which sectors to focus their R&D activity on market size effect

Zs´ ofia L. B´ ar´ any (Sciences Po)

The Minimum Wage and Inequality

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Key Ingredients Two sector production economy I I

high-skilled workers work in one sector, low-skilled workers in the other the two goods they produce are imperfect substitutes

Minimum wage I

I

workers with marginal product lower than the minimum wage are unemployed everyone else employed in the sector relevant for their skill

Endogenous skill acquisition I

individuals make educational decisions optimally - based on idiosyncratic cost and ability

Endogenous technology I

I

technical change is based on choices made by firms about which sectors to focus their R&D activity on market size effect

Main idea: changes in the minimum wage affect the earnings and employment opportunities differentially across education groups. Zs´ ofia L. B´ ar´ any (Sciences Po)

The Minimum Wage and Inequality

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Mechanisms - as a reaction to a lower minimum wage 1

Skill composition changes

2

Ability composition changes

3

Directed technology effect

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Mechanisms - as a reaction to a lower minimum wage 1

Skill composition changes I I

I

inflow from unemployment to the low-skilled labour market → low-skilled wages decrease → more education acquisition for those with high enough ability → easier to find employment → less education acquisition at the low end

2

Ability composition changes

3

Directed technology effect

Zs´ ofia L. B´ ar´ any (Sciences Po)

The Minimum Wage and Inequality

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Mechanisms - as a reaction to a lower minimum wage 1

Skill composition changes I I

I

2

Ability composition changes I I

I 3

inflow from unemployment to the low-skilled labour market → low-skilled wages decrease → more education acquisition for those with high enough ability → easier to find employment → less education acquisition at the low end lower ability workers enter the workforce, widening the range of abilities both labour supplies expand, the average ability in both sectors decreases the average ability in the low-skilled labour market decreases more

Directed technology effect

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The Minimum Wage and Inequality

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Mechanisms - as a reaction to a lower minimum wage 1

Skill composition changes I I

I

2

Ability composition changes I I

I 3

inflow from unemployment to the low-skilled labour market → low-skilled wages decrease → more education acquisition for those with high enough ability → easier to find employment → less education acquisition at the low end lower ability workers enter the workforce, widening the range of abilities both labour supplies expand, the average ability in both sectors decreases the average ability in the low-skilled labour market decreases more

Directed technology effect I

I I

the expansion of the low-skilled labour force dominates, leading to a decrease in the relative supply of skilled labour this makes technology less skill-biased quantitatively very small

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The Minimum Wage and Inequality

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Quantitative Results The fall in minimum wages explains the following fraction of the changes observed in the data from 1981 until 70% 60% 50% 40% 30% 20% 10% 0% 1986

Zs´ ofia L. B´ ar´ any (Sciences Po)

1991

1996

2001

average skill premium

90th/10th percentile

50th/10th percentile

90th/50th percentile

The Minimum Wage and Inequality

2006

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Related Literature I.

Theory

endogenous skill formation, exogenous technology Heckman, Lochner, Taber (1998), Caselli (1999), Galor & Moav (2000), ´ ah´ Abr´ am (2008)

exogenous skill formation, endogenous technology Acemoglu (1998,2002), Kiley (1999)

capital-skill complementarity Krusell, Ohanian, R´ıos-Rull, Violante (2000)

effects of minimum wage on human capital Cahuc and Michel (1996), Ravn and Sorensen (1999)

I allow both skill formation and technology to be endogenous.

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Related Literature II. Empirics

the effects of skill biased technical change on wage inequality in support: Katz&Murphy (1992), Juhn et al (1993), Krueger (1993), Berman et al (1994), Autor, Katz, Krueger (1998), Autor, Katz, Kearney (2005, 2008) against: Card&DiNardo (2002), Beaudry&Green (2005), Lemieux (2006)

the effects of minimum wages on wage inequality DiNardo, Fortin & Lemieux (1996), Lee (1999), Card & DiNardo (2002), Autor, Manning, Smith (2009)

the effects of minimum wages on unemployment negative: Brown et al (1982), Wellington (1991), Neumark & Wascher (1992, 2000), Baker, Benjamin, Stanger (1999) none or small positive: Card (1992), Card & Krueger (1994, 2000), Machin & Manning (1994)

the effects of minimum wages on educational attainment Neumark & Wascher (2003), Neumark & Nizalova (2007), Sutch (2007) Zs´ ofia L. B´ ar´ any (Sciences Po)

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Road map

1

Model

2

Steady State

3

Calibration

4

Results

5

Decomposition

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The Minimum Wage and Inequality

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Overview - Production Final good produced from the two intermediate goods; perfect competition

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The Minimum Wage and Inequality

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Overview - Production Final good produced from the two intermediate goods; perfect competition High- and low-skilled intermediate goods produced using available labour, machines; perfect competition

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The Minimum Wage and Inequality

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Overview - Production Final good produced from the two intermediate goods; perfect competition High- and low-skilled intermediate goods produced using available labour, machines; perfect competition Patent owners produce and sell machines; monopolists profits are increasing in the amount of labour that can use the machine

Zs´ ofia L. B´ ar´ any (Sciences Po)

The Minimum Wage and Inequality

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Overview - Production Final good produced from the two intermediate goods; perfect competition High- and low-skilled intermediate goods produced using available labour, machines; perfect competition Patent owners produce and sell machines; monopolists profits are increasing in the amount of labour that can use the machine R&D firms invest in improving the quality of machines; free entry more investment into bigger sector, market size effect success → become monopolist patent owners skip Zs´ ofia L. B´ ar´ any (Sciences Po)

The Minimum Wage and Inequality

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Production - Perfect Competition Final good: 

l ρ

h ρ

Y = (Y ) + γ(Y )

1

ρ

where ρ < 1. Intermediate good for s ∈ {l, h}: Y s = As (N s )β =

1 1−β

R

1 s,j s,j 1−β dj 0 q (x )



(N s )β

where N s - efficiency units of labour in sector s q s,j - quality of line j, sector s machines x s,j - quantity of line j, sector s machines

Zs´ ofia L. B´ ar´ any (Sciences Po)

The Minimum Wage and Inequality

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Patent Owners - Monopolists Machines are produced and sold by the patents owners. Only the best quality machine is sold at its monopoly price in each line j. Per period profit for the owner is: π j,s = q j,s β(1 − β)

1−β β

1

(p s ) β N s

for s = l, h

The value of owning the leading vintage of quality q in sector s is: Vtj,s (q) = πtj,s + P(q the best quality at t + 1)

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The Minimum Wage and Inequality

1 V j,s (q) 1 + r t+1

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R&D - Technological Advances

Quality ladder model: each innovation improves the quality of an existing line by a fixed factor, q > 1 if R&D firm k invests zkj units to improve line j, the innovation has Poisson arrival rate ηzkj the cost of investing one unit into R&D to invent a machine of quality q is Bq

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The Minimum Wage and Inequality

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Free entry into the R&D sector ⇒ the expected profit from R&D has to be zero: j,s zt,k (q) 

z tj,s (q) |

j,s

1 − e −ηz t {z

(q)

probability of success

1 s,j j,s Et (Vt+1 (q)) = Bqzt,k (q) 1 + r {z } | {z } }|



present value return

cost

where s,j Et (Vt+1 (q)) - the expected value of owning the leading vintage of quality q in line j in sector s at time t + 1

r - the interest rate z j,s t (q) - the total investment on line j in sector s at time t

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The Minimum Wage and Inequality

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Labour Supply Demographic structure every period a new generation of size 1 − λ is born the survival probability is λ from one period to the next heterogeneity in ability and in the time cost of education

Zs´ ofia L. B´ ar´ any (Sciences Po)

The Minimum Wage and Inequality

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Labour Supply Demographic structure every period a new generation of size 1 − λ is born the survival probability is λ from one period to the next heterogeneity in ability and in the time cost of education Due to perfect competition everyone is paid their marginal product: w s (ai ) = ai β(1 − β)

Zs´ ofia L. B´ ar´ any (Sciences Po)

1−2β β

1

(p s ) β Q s ≡ ai w s

The Minimum Wage and Inequality

for s = l, h

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Labour Supply Demographic structure every period a new generation of size 1 − λ is born the survival probability is λ from one period to the next heterogeneity in ability and in the time cost of education Due to perfect competition everyone is paid their marginal product: w s (ai ) = ai β(1 − β)

1−2β β

1

(p s ) β Q s ≡ ai w s

for s = l, h

Minimum wage w set by the government: if w s (a) < w → unemployed. Unemployment depends on: ability → a education → w s

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The Minimum Wage and Inequality

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There is a cutoff ability of unemployment for both the high- and low-skilled: w as ≡ s w Decision at birth whether to acquire education or not Cost education takes ci periods → no earnings Benefit education grants access to the high-skilled labour market Two potential reasons for acquiring education: higher wage better protection from unemployment Individuals choose their education to maximize: j ∞  X λ yt+j Et 1+r j=0

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The Minimum Wage and Inequality

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Equilibrium - Steady State

The economy is in a decentralized equilibrium at all times: all sectors maximize their profits individuals maximize their lifetime utility given a sequence of minimum wages.

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The Minimum Wage and Inequality

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Equilibrium - Steady State

The economy is in a decentralized equilibrium at all times: all sectors maximize their profits individuals maximize their lifetime utility given a sequence of minimum wages. Steady state: decentralized equilibrium where all variables are constant or grow at a constant rate.

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The Minimum Wage and Inequality

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Equilibrium - Steady State

The economy is in a decentralized equilibrium at all times: all sectors maximize their profits individuals maximize their lifetime utility given a sequence of minimum wages. Steady state: decentralized equilibrium where all variables are constant or grow at a constant rate. Analyse the effects of a permanent unexpected drop in the minimum wage: change of steady state and transitional dynamics.

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Production The relative quality is constant in the steady state: 1 Q h∗ Q = tl∗ = γ 1−ρ Qt

∗



N h∗ N l∗

βρ  1−ρ

The relative price is: p h∗ p = l∗ = p ∗



N h∗ N l∗

−β

The skill premium per efficiency unit of labour is: 1

1 p h∗ β Qth∗ wth∗ = = γ 1−ρ l∗ l∗ l∗ p wt Qt

Zs´ ofia L. B´ ar´ any (Sciences Po)



N h∗ N l∗

The Minimum Wage and Inequality

βρ  1−ρ −1

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Unemployment thresholds: w t = ah∗ wth∗ = al∗ wtl∗ As wth∗ > wtl∗ ⇒ ah∗ < al∗

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The Minimum Wage and Inequality

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Unemployment thresholds: w t = ah∗ wth∗ = al∗ wtl∗ As wth∗ > wtl∗ ⇒ ah∗ < al∗ Three cases: 1 a < ah∗ ⇒ unemployed anyway ⇒ no education

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The Minimum Wage and Inequality

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Unemployment thresholds: w t = ah∗ wth∗ = al∗ wtl∗ As wth∗ > wtl∗ ⇒ ah∗ < al∗ Three cases: 1 a < ah∗ ⇒ unemployed anyway ⇒ no education 2 a ∈ [ah∗ , al∗ ) ⇒ unemployed or high-skilled worker ⇒ become high-skilled

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The Minimum Wage and Inequality

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Unemployment thresholds: w t = ah∗ wth∗ = al∗ wtl∗ As wth∗ > wtl∗ ⇒ ah∗ < al∗ Three cases: 1 a < ah∗ ⇒ unemployed anyway ⇒ no education 2 a ∈ [ah∗ , al∗ ) ⇒ unemployed or high-skilled worker ⇒ become high-skilled 3 a ≥ al∗ ⇒ never unemployed, high or low-skilled worker ⇒ become high-skilled if s s ∞  ∞  X X λ λ h∗ h∗ l∗ wt+s + a(1 − c)wt ≥ a wt+s a 1+r 1+r s=1

s=0

can be simplified to: ∗

c ≤c ≡ c ∗:

1− 1−

wtl∗ wth∗ g ∗λ 1+r

cutoff time cost for education, constant, independent of ability

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The Minimum Wage and Inequality

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c

a

Figure: Optimal education

Zs´ ofia L. B´ ar´ any (Sciences Po)

The Minimum Wage and Inequality

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c

a

ah∗

Figure: Optimal education

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The Minimum Wage and Inequality

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c

U

a

ah∗

Figure: Optimal education

Zs´ ofia L. B´ ar´ any (Sciences Po)

The Minimum Wage and Inequality

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c

U

a

ah∗ al∗

Figure: Optimal education

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The Minimum Wage and Inequality

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c

U

N h∗

a

ah∗ al∗

Figure: Optimal education

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The Minimum Wage and Inequality

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c

N l∗

c∗

U

N h∗

N h∗ a

ah∗ al∗

Figure: Optimal education

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The Minimum Wage and Inequality

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c

N l∗

c∗

U

N h∗ a

ah∗ al∗

Figure: Optimal education

Zs´ ofia L. B´ ar´ any (Sciences Po)

The Minimum Wage and Inequality

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Lower Minimum Wage

A lower minimum wage implies: easier to find employment → lower al , ah → previously unemployed flow into the low-skilled labour market ⇒ increase in skill premium ⇒ increases educational attainment at higher parts of ability distribution easier to find employment at very low end of ability distribution → fewer people acquire education as new generations are born, convergence towards new steady state

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The Minimum Wage and Inequality

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c

c0∗

a

l∗

a0h∗ a0

Figure: Change in the optimal education and labour market participation

lighter colours - generations born before announcement darker colours - generations born after announcement Zs´ ofia L. B´ ar´ any (Sciences Po)

The Minimum Wage and Inequality

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c

c1∗ c0∗

a

l∗

a1h∗a1l∗ a0h∗ a0

Figure: Change in the optimal education and labour market participation

lighter colours - generations born before announcement darker colours - generations born after announcement Zs´ ofia L. B´ ar´ any (Sciences Po)

The Minimum Wage and Inequality

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c

c1∗ c0∗

a

l∗

a1h∗a1l∗ a0h∗ a0

Figure: Change in the optimal education and labour market participation

lighter colours - generations born before announcement darker colours - generations born after announcement Zs´ ofia L. B´ ar´ any (Sciences Po)

The Minimum Wage and Inequality

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c

c1∗ c0∗

a

l∗

a1h∗a1l∗ a0h∗ a0

Figure: Change in the optimal education and labour market participation

lighter colours - generations born before announcement darker colours - generations born after announcement Zs´ ofia L. B´ ar´ any (Sciences Po)

The Minimum Wage and Inequality

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c

c1∗ c0∗

a

l∗

a1h∗a1l∗ a0h∗ a0

Figure: Change in the optimal education and labour market participation

lighter colours - generations born before announcement darker colours - generations born after announcement Zs´ ofia L. B´ ar´ any (Sciences Po)

The Minimum Wage and Inequality

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c

c1∗ c0∗

a

l∗

a1h∗a1l∗ a0h∗ a0

Figure: Change in the optimal education and labour market participation

lighter colours - generations born before announcement darker colours - generations born after announcement Zs´ ofia L. B´ ar´ any (Sciences Po)

The Minimum Wage and Inequality

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c

c1∗ c0∗

a

l∗

a1h∗a1l∗ a0h∗ a0

Figure: Change in the optimal education and labour market participation

lighter colours - generations born before announcement darker colours - generations born after announcement Zs´ ofia L. B´ ar´ any (Sciences Po)

The Minimum Wage and Inequality

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c

c1∗ c0∗

a

l∗

a1h∗a1l∗ a0h∗ a0

Figure: Change in the optimal education and labour market participation

lighter colours - generations born before announcement darker colours - generations born after announcement Zs´ ofia L. B´ ar´ any (Sciences Po)

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Calibration

e and the The parameters that need to be calibrated: r , λ, β, ρ, γ, q, η, B, w parameters of the ability and cost factor distribution. Parameters set outside the model: one period is set to be 5 years, λ is set to match 45 working years on average → λ = 8/9 the real interest rate is around 5 percent per year → r = 1.055 − 1 the wage bill in the US is around 2/3 of the total output → β = 2/3

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The Minimum Wage and Inequality

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Ability and cost distribution

0

kdensity wage .5 1

1.5

Neither ability, nor cost is observable. Good starting point for choosing the distributions is:

0

2

4

6

8

10

log wage low−skilled

Zs´ ofia L. B´ ar´ any (Sciences Po)

high−skilled

The Minimum Wage and Inequality

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Assumptions: cost and ability distribution are independent ability log normally distributed time cost uniformly distributed on [0, c] I normalize the mean of the ability distribution to be 1. Wage equation: w s (a) = aw s

⇒ w s = as w s

Define relative ability as: e ais ≡

Zs´ ofia L. B´ ar´ any (Sciences Po)

ai w s (ai ) = as ws

The Minimum Wage and Inequality

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c Ll∗ c∗

U Lh∗ a

ah∗al∗

Given a cost and ability distribution U, Lh , Ll pin down ah∗ , al∗ and c ∗ .

ah =

Nh Lh

al =

Nl Ll

The ability of individual i working in sector s is then: ais = e ais as = Zs´ ofia L. B´ ar´ any (Sciences Po)

w s (ai ) s a ws

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The likelihood of observing a d year old high-skilled person with wage w h (i) is: L(w h (i), d) =  0     f  (aih ) f (aih )G ( d−18 5 )  h )G (c ∗ )  f (a  i   f (aih )G (min{c ∗ , d−18 5 })

if aih < ah∗ h if ai ∈ [ah∗ , al∗ ) if aih ∈ [ah∗ , al∗ ) if aih ≥ al∗ if aih ≥ al∗

& & & &

d d d d

≥ 23 < 23 ≥ 23 < 23

c

c∗

ah∗ al∗ Zs´ ofia L. B´ ar´ any (Sciences Po)

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The likelihood of observing a d year old high-skilled person with wage w h (i) is: L(w h (i), d) =  0     f  (aih ) f (aih )G ( d−18 5 )  h )G (c ∗ )  f (a  i   f (aih )G (min{c ∗ , d−18 5 })

if aih < ah∗ h if ai ∈ [ah∗ , al∗ ) if aih ∈ [ah∗ , al∗ ) if aih ≥ al∗ if aih ≥ al∗

& & & &

d d d d

≥ 23 < 23 ≥ 23 < 23

c

c∗

ah∗ al∗ Zs´ ofia L. B´ ar´ any (Sciences Po)

The Minimum Wage and Inequality

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The likelihood of observing a d year old high-skilled person with wage w h (i) is: L(w h (i), d) =  0     f  (aih ) f (aih )G ( d−18 5 )  h )G (c ∗ )  f (a  i   f (aih )G (min{c ∗ , d−18 5 })

if aih < ah∗ h if ai ∈ [ah∗ , al∗ ) if aih ∈ [ah∗ , al∗ ) if aih ≥ al∗ if aih ≥ al∗

& & & &

d d d d

≥ 23 < 23 ≥ 23 < 23

c

c∗

ah∗aihal∗ Zs´ ofia L. B´ ar´ any (Sciences Po)

The Minimum Wage and Inequality

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The likelihood of observing a d year old high-skilled person with wage w h (i) is: L(w h (i), d) =  0     f  (aih ) f (aih )G ( d−18 5 )  h )G (c ∗ )  f (a  i   f (aih )G (min{c ∗ , d−18 5 })

if aih < ah∗ h if ai ∈ [ah∗ , al∗ ) if aih ∈ [ah∗ , al∗ ) if aih ≥ al∗ if aih ≥ al∗

& & & &

d d d d

≥ 23 < 23 ≥ 23 < 23

c d−18 5

c∗

ah∗aihal∗ Zs´ ofia L. B´ ar´ any (Sciences Po)

The Minimum Wage and Inequality

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The likelihood of observing a d year old high-skilled person with wage w h (i) is: L(w h (i), d) =  0     f  (aih ) f (aih )G ( d−18 5 )  h )G (c ∗ )  f (a  i   f (aih )G (min{c ∗ , d−18 5 })

if aih < ah∗ h if ai ∈ [ah∗ , al∗ ) if aih ∈ [ah∗ , al∗ ) if aih ≥ al∗ if aih ≥ al∗

& & & &

d d d d

≥ 23 < 23 ≥ 23 < 23

c

c∗

ah∗ al∗ Zs´ ofia L. B´ ar´ any (Sciences Po)

aih

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The likelihood of observing a d year old high-skilled person with wage w h (i) is: L(w h (i), d) =  0     f  (aih ) f (aih )G ( d−18 5 )  h )G (c ∗ )  f (a  i   f (aih )G (min{c ∗ , d−18 5 })

if aih < ah∗ h if ai ∈ [ah∗ , al∗ ) if aih ∈ [ah∗ , al∗ ) if aih ≥ al∗ if aih ≥ al∗

& & & &

d d d d

≥ 23 < 23 ≥ 23 < 23

c

c∗ d−18 5

ah∗ al∗ Zs´ ofia L. B´ ar´ any (Sciences Po)

aih

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Similarly for a low-skilled person:  0 if ail < al∗ l L(w (i)) = l ∗ f (ai )(1 − G (c )) if ail ≥ al∗ Data: Current Population Survey Outgoing Rotation Group supplements, 1981 high-skilled: those who have some years of college low-skilled: everyone else skill category and employment status → fraction of unemployed, studying, low-skilled and high-skilled workers wage: the residual from regressing the log hourly wages on age, age quadratic, sex and race Values: c = 0.82 σ = 0.73 Zs´ ofia L. B´ ar´ any (Sciences Po)

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Remaining parameters calibrated by minimizing the weighted distance of initial BGP moments from the 1981 data moments. Table: Moments and calibrated parameters

Moment Lu Ll Lh g w h /w l w /w50 w90 /w50 w50 /w10 w h /w

Data 0.0693 0.5338 0.3554 0.0800 1.3344 1.1072 1.7060 1.7006 1.1796

Zs´ ofia L. B´ ar´ any (Sciences Po)

Model 0.1023 0.4923 0.3964 0.0798 1.0518 1.2942 2.4252 2.0778 1.0280

ρ 0.9

γ 1.15

The Minimum Wage and Inequality

η 0.05

q 2.08

B 0.15

e w 0.4

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Transitional Dynamics

The real value of the minimum wage declined by about 30% after 1981, 20% decline relative to the average low-skilled wage graph initial steady state - 1981 new steady state - 20% lower minimum wage

The transitional dynamics are done as in Schmitt-Grohe and Uribe (2004). Second order approximation of the equations that govern the transitional dynamics around the new steady state.

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high−skilled unemployment cutoff

low−skilled unemployment cutoff

0.4

0.4

0.3

0.3

0.2 1980

2000

2020

2040

2060

0.2 1980

2000

c*

2020

2040

2060

skill premium 1.1

0.37

1.099

0.365

1.098 0.36 1980

2000

2020

2040

2060

1980

2000

2020

2040

2060

2040

2060

2040

2060

Qh/Ql

Nh/Nl 0.771 0.77

0.8465

0.769 0.768 1980

2000

2020

2040

2060

0.8455 1980

2000

h

2020 Nl

N 0.426

0.554

0.424 0.422 0.42 1980

0.548 2000

2020

2040

2060

1980

2000

pl

2020

growth rates 1.084

1.0242 1.082

1.0242 1.0242 1980

gh gl

1.08 2000

2020

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1980

2000

The Minimum Wage and Inequality

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Average skill premium average skill premium 1.04 1.035 1.03 1.025 1.02 1.015 1.01 1.005 1 1980

1990

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Relative percentiles 1.1 1.09 1.08 1.07 1.06 1.05 1.04 1.03 1.02 1.01 1 1980

1990

2000

2010

90/50

2020

2030

2040

50/10

2050

2060

2070

90/10

data Zs´ ofia L. B´ ar´ any (Sciences Po)

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Decomposition

Three simplified versions of the full model (blue): 1

Education & technology exogenous (black)

2

Education exogenous, technology endogenous (green)

3

Education endogenous, technology exogenous (red)

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Decomposition — skill premium 1.05 1.045 1.04 1.035 1.03 1.025 1.02 1.015 1.01 1.005 1 1980 full model

1990

2000

2010

exogenous education

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exogenous technology

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2060

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exogenous educ & tech

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Decomposition — wage gaps 90/10

50/10

1.1

1.08

1.08

1.06

1.06 1.04 1.04 1.02

1.02 1 1980

2000

2020

2040

2060

1 1980

2000

2020

2040

2060

90/50 1.03 full model 1.02

exogenous education exogenous technology

1.01

exogenous educ & tech 1 1980

2000

2020

2040

2060

robustness Zs´ ofia L. B´ ar´ any (Sciences Po)

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Concluding remarks I developed a general equilibrium framework where both technology and education are endogenous. In such a framework the minimum wage not only shifts the truncation point of the wage distribution, but alters the incentives for acquiring education for everyone. The drop in the value of the minimum wage has a significant impact on the skill premium and on the distribution of wages in the short run in the long run the effect on the wage distribution is more persistent The decomposition shows that the initial impact is largely driven by the inflow from unemployment into the low-skilled market the directed technology effect is quantitatively small the adjustment of educational attainment increases the effect of minimum wages on inequality over time Zs´ ofia L. B´ ar´ any (Sciences Po)

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Thank you!

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Rising wage inequality 1.35 1.3

1.25 1.2 1.15 1.1

1.05 1 0.95 1973

back

1978

1983

1988

1993

1998

2003

90th/50th percentile

50th/10th percentile

90th/10th percentile

skill premium

back II.

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Minimum wage 6.7

0.53

6.2

0.48

5.7 0.43

5.2 4.7

0.38

4.2

0.33

3.7

0.28

3.2 0.23

2.7 2.2

0.18 1973

1978

1983

1988

1993

1998

2003

real minimum wage minimum wage/average low-skilled wage minimum wage/average high-skilled wage back I.

back II.

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Observed skill premium 1.04 ρ=0.92 ρ=0.65 ρ=0.65,γ=1.05 ρ=0.75 ρ=0.8

1.035

1.03

1.025

1.02

1.015

1.01

1.005

1 1980

1990

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2020

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90-10 wage gap 1.1 1.09 1.08 1.07 1.06 1.05 1.04 1.03

ρ=0.92 ρ=0.65 ρ=0.65,γ=1.05 ρ=0.75 ρ=0.8

1.02 1.01 1 1980

1990

2000

2010

2020

2030

2040

2050

2060

2070

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Observed skill premium 1.04 γ=1.15 γ=0.95 γ=1.05 γ=1.25 γ=1.35

1.035

1.03

1.025

1.02

1.015

1.01

1.005

1 1980

1990

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90-10 wage gap 1.1 1.09 1.08 1.07 1.06 1.05 1.04 γ=1.15

1.03

γ=0.95 γ=1.05 γ=1.25 γ=1.35

1.02 1.01 1 1980

1990

2000

2010

2020

2030

2040

2050

2060

2070

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Observed skill premium 1.05 σ=0.72 σ=0.6 σ=0.7 σ=0.75 σ=0.8 σ=0.85

1.045 1.04 1.035 1.03 1.025 1.02 1.015 1.01 1.005 1 1980

1990

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90-10 wage gap 1.12

1.1

1.08

1.06

1.04

σ=0.72 σ=0.6 σ=0.7

1.02

σ=0.75 σ=0.8 σ=0.85

1 1980

1990

2000

2010

2020

2030

2040

2050

2060

2070

back Zs´ ofia L. B´ ar´ any (Sciences Po)

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